Doubly excited electron configuration

The H2 MO function gives equal weight to covalent and ionic terms and thus underestimates electron correlation, which acts to keep electrons apart and makes the ionic terms less important than the covalent terms. The MO function can be improved by configuration interaction the most important excited CSF is that from the doubly excited electron configuration (trjls). The H2 covalent VB wave function can be improved by the addition of a contribution from ionic terms. 

Configuration 1 is the ground configuration, 2 and 3 are singly excited, and 4 is doubly excited. Electron interaction places 2 at higher energy than the triplet 3 (Hund s rule). Configuration interaction mixes 1 and 4. 

Flexible thiones such as PT decay more rapidly than the rigid thiones because in such species an additional doubly excited (two-excited electron configuration) state lies below the Sj state and provides an additional fast relaxation path [60,79],... 

Let us consider another example. In describmg the n electron pair of an olefin, it is important to mix in doubly excited configurations of the fomi (n ). The physical importance of such configurations can again be made clear by using the identity... 

The amount of computation for MP2 is determined by the partial transformation of the two-electron integrals, what can be done in a time proportionally to m (m is the number of basis functions), which is comparable to computations involved in one step of CID (doubly-excited configuration interaction) calculation. To save some computer time and space, the core orbitals are frequently omitted from MP calculations. For more details on perturbation theory please see A. Szabo and N. Ostlund, Modem Quantum Chemistry, Macmillan, New York, 1985. 

Fig. 1.11. Ground state and excited charge resonant states of a model doubly-charged diatomic molecule. The electronic configurations of the states are shown schematically in a 1-D double-well potential...

Notwithstanding, after hydrogen, helium is also the simplest naturally available atomic species, which, in contrast to one electron atoms, exhibits the additional electron-electron interaction, as a source of electronic correlations. Hence, helium is one of the simplest systems where electronic correlations can be studied. Direct manifestations of electronic correlations have been found, e.g., in doubly excited states of helium localized along highly asymmetric, though very stable, frozen planet configurations (FPC) (K. Richter et.al., 1990), or scarred by... 

Another well-defined configuration of the classical three body Coulomb problem with unambiguous quantum correspondence is the collinear antisymmetric stretch configuration, where the electrons are located on opposite sides of the nucleus. In contrast to the frozen planet orbit, the antisymmetric stretch is unstable in the axial direction (G.S. Ezra et.al., 1991 P. Schlagheck et.al., 2003), with the two electrons colliding with the nucleus in a perfectly alternating way (Fig. 3 (left)). Hence, already the one dimensional treatment accounts for the dominant classical decay channel of this configuration. As for the frozen planet, there are doubly excited states of helium associated to the periodic orbit of the ASC as illustrated in Fig. 3 (left). 

In this paper we examined quantum aspects of special classical configurations of two-electron atoms. In the doubly excited regime, we found quantum states of helium that are localized along ID periodic orbits of the classical system. A comparison of the decay rates of such states obtained in one, two and three dimensional ab initio calculations allows us to conclude that the dimension of the accessible configuration space does matter for the quantitative description of the autoionization process of doubly excited Rydberg states of helium. Whilst ID models can lead to dramatically false predictions for the decay rates, the planar model allows for a quantitatively reliable reproduction of the exact life times. 

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